Solutions can be ideal or non-ideal, affecting their behavior. Ideal solutions follow Raoult's and Henry's laws, assuming no interactions between components. Non-ideal solutions deviate from these laws due to molecular interactions, requiring activity coefficients and to describe their behavior.
Models like , Van Laar, and Margules equations help predict non-ideal solution behavior. These models use parameters to account for deviations from ideality, allowing for more accurate predictions of thermodynamic properties in real-world applications.
States that the of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its in the solution
Mathematically expressed as pi=xipi∗, where pi is the partial vapor pressure of component i, xi is the mole fraction of component i, and pi∗ is the vapor pressure of pure component i
Assumes no intermolecular interactions between different components in the solution
Applicable to solutions where the components have similar molecular sizes and intermolecular forces (ethanol and water)
Henry's Law
Describes the solubility of a gas in a liquid at a given temperature
States that the amount of dissolved gas is directly proportional to the partial pressure of the gas above the liquid
Mathematically expressed as c=kP, where c is the concentration of the dissolved gas, P is the partial pressure of the gas, and k is constant, which depends on the solute, solvent, and temperature
Assumes that the gas molecules do not interact with each other in the solution
Applicable to dilute solutions where the solute is a gas and the solvent is a liquid (carbon dioxide in water)
Non-Ideal Solutions
Activity Coefficient
A factor that accounts for the deviation of a solution from ideal behavior
Defined as the ratio of the actual fugacity (or activity) of a component to its ideal fugacity (or activity)
Mathematically expressed as γi=xifi∗fi, where γi is the of component i, fi is the fugacity of component i in the solution, xi is the mole fraction of component i, and fi∗ is the fugacity of pure component i
A value of 1 indicates ideal behavior, while values greater than 1 indicate positive deviations and values less than 1 indicate negative deviations from ideality
Depends on the composition of the solution and the intermolecular interactions between components (ethanol and water at high concentrations)
Excess Properties
Thermodynamic properties that describe the deviation of a solution from ideal behavior
Defined as the difference between the actual value of a property and the value it would have in an ideal solution
Examples include excess Gibbs free energy (GE), excess enthalpy (HE), and excess entropy (SE)
Mathematically expressed as ME=M−Mid, where ME is the excess property, M is the actual value of the property, and Mid is the value of the property in an ideal solution
Provide insights into the nature and strength of intermolecular interactions in the solution (mixing of ethanol and water results in a negative excess enthalpy)
Deviation from Ideality
Occurs when the properties of a solution deviate from those predicted by ideal solution laws ( and Henry's law)
Can be caused by differences in molecular size, shape, or intermolecular forces between components
Positive deviations occur when the intermolecular attractions between unlike molecules are weaker than those between like molecules, leading to higher vapor pressures and lower boiling points than predicted (acetone and chloroform)
Negative deviations occur when the intermolecular attractions between unlike molecules are stronger than those between like molecules, leading to lower vapor pressures and higher boiling points than predicted (chloroform and ethanol)
The extent of deviation depends on the nature and concentration of the components in the solution
Models for Non-Ideal Solutions
Regular Solutions
A model that accounts for the non-ideality of solutions caused by differences in intermolecular forces between components
Assumes that the excess entropy of mixing is zero (SE=0) and that the excess enthalpy of mixing is proportional to the product of the mole fractions of the components
Mathematically expressed as GE=x1x2Λ, where GE is the excess Gibbs free energy, x1 and x2 are the mole fractions of components 1 and 2, and Λ is a parameter that depends on the intermolecular interactions between the components
Provides a simple way to estimate the activity coefficients and of non-ideal solutions (hexane and benzene)
Limited to solutions where the components have similar molecular sizes and shapes
Van Laar Equation
An empirical model that describes the excess Gibbs free energy of non-ideal solutions
Assumes that the excess Gibbs free energy is a function of the mole fractions and two adjustable parameters, A and B
Mathematically expressed as RTGE=x1+Bx2Ax1x2+Bx1+x2Bx1x2, where GE is the excess Gibbs free energy, R is the gas constant, T is the temperature, x1 and x2 are the mole fractions of components 1 and 2, and A and B are adjustable parameters that depend on the components and temperature
Provides a better fit to experimental data than the regular solution model for solutions with moderate deviations from ideality (ethanol and water)
Requires the determination of the adjustable parameters from experimental data
Margules Equation
An empirical model that describes the excess Gibbs free energy of non-ideal solutions
Assumes that the excess Gibbs free energy is a polynomial function of the mole fractions and adjustable parameters
The two-suffix is mathematically expressed as RTGE=x1x2(A12+B12(x1−x2)), where GE is the excess Gibbs free energy, R is the gas constant, T is the temperature, x1 and x2 are the mole fractions of components 1 and 2, and A12 and B12 are adjustable parameters that depend on the components and temperature
The three-suffix Margules equation includes an additional term with a third adjustable parameter to better describe solutions with large deviations from ideality (acetone and chloroform)
Provides a flexible and accurate way to model the thermodynamic properties of non-ideal solutions
Requires the determination of the adjustable parameters from experimental data